{"paper":{"title":"On Metrizing Vague Convergence of Random Measures with Applications on Bayesian Nonparametric Models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Luai Al-Labadi","submitted_at":"2016-10-10T20:25:26Z","abstract_excerpt":"This paper deals with studying vague convergence of random measures of the form $\\mu_{n}=\\sum_{i=1}^{n} p_{i,n} \\delta_{\\theta_i}$, where $(\\theta_i)_{1\\le i \\le n}$ is a sequence of independent and identically distributed random variables with common distribution $\\Pi$, $(p_{i,n})_{1 \\le i \\le n}$ are random variables chosen according to certain procedures and are independent of $(\\theta_i)_{i \\geq 1}$ and $\\delta_{\\theta_i}$ denotes the Dirac measure at $\\theta_i$. We show that $\\mu_{n}$ converges vaguely to $\\mu=\\sum_{i=1}^{\\infty} p_{i} \\delta_{\\theta_i}$ if and only if $\\mu^{(k)}_{n}=\\sum"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.03083","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}